Obtain the resonant frequency and Q-factor of a series LCR circuit with L = 3.0 H, C = 27 μF, and R = 7.4Ω. It is desired to improve the sharpness of the resonance of the circuit by reducing its ‘full width at half maximum’ by a factor of 2. Suggest a suitable way.

Question

Philoid · Accepted Answer

Given: L = 3.0 H

C = 27 μF,

In Farad, capacitance C = 27 × 10^-6F

R = 7.4Ω

Angular frequency is given by the relation:

ω_R = 1/√LC

ω_R = 1(√27 × 10^-6F × 3 H)

On calculating, we get

ω_R = 111.11 rad/s

_{Q factor can be calculated as follows:}

_{Q = ω}_RL/R

_{Q = (111.11(rad/s) × 3H)/7.4(Ω)}

_⇒ _{Q = 45.0446}

The sharpness of the resonance of the circuit by reducing its ‘full width at half maximum’ by a factor of 2 by reducing R to half.

i.e. R = R/2 = 7.4(Ω)/2 = 3.7Ω